Re-UV with SmartUV after scaling UV island
Perhaps you could:


Select everything except the interior, then U Smart UV Project.
Select the interior and again U Smart UV Project.
Scale down and move this second unwrap where you want, or even, if you don't want to manage 2 UVs overlaying, give it a second material (with the same Image Texture).
Note that you could use Vertex Groups to facilitate the selections.
Also, in the UV/Image Editor, enable Keep UV And Edit Mode Mesh Selection In Synch so that you can see both the 2 UVs.